{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VLU6E2ZHN5CC3KITRXG3KLIE6F","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4fffae2a322188c2d947a3ede0f70a8e2ba26628606326257d7bf9b60d6d45d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-29T18:07:04Z","title_canon_sha256":"93e140c081a568148132d9d8861ca4e15c932c5f3032ec345631a38f4553db81"},"schema_version":"1.0","source":{"id":"1309.7634","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7634","created_at":"2026-05-18T02:55:48Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7634v2","created_at":"2026-05-18T02:55:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7634","created_at":"2026-05-18T02:55:48Z"},{"alias_kind":"pith_short_12","alias_value":"VLU6E2ZHN5CC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VLU6E2ZHN5CC3KIT","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VLU6E2ZH","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:701f731ccf353467f295f5c41db4cdec89df7ba61189cf2c481b7f0bc1504d08","target":"graph","created_at":"2026-05-18T02:55:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as $t\\to \\infty$. It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree.","authors_text":"Carolina A. Mosquera, Julio D. Rossi, Leandro M. Del Pezzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-29T18:07:04Z","title":"Existence, uniqueness and decay rates for evolution equations on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7634","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f369c50d18194712bd4ff5024563bd6baf775e72297d99dda9aa0b2d053763f1","target":"record","created_at":"2026-05-18T02:55:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4fffae2a322188c2d947a3ede0f70a8e2ba26628606326257d7bf9b60d6d45d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-29T18:07:04Z","title_canon_sha256":"93e140c081a568148132d9d8861ca4e15c932c5f3032ec345631a38f4553db81"},"schema_version":"1.0","source":{"id":"1309.7634","kind":"arxiv","version":2}},"canonical_sha256":"aae9e26b276f442da9138dcdb52d04f1562d6e976bbc73a7bebf88198704e933","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aae9e26b276f442da9138dcdb52d04f1562d6e976bbc73a7bebf88198704e933","first_computed_at":"2026-05-18T02:55:48.353763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:48.353763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5MOxgB1NHP1YuzLN9CD4UPyvc+EfvVjy6rx+RHP1JJmPBn2asvVTivC+8kF9JgnTUvOz0BjphemUC3ecPVJVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:48.354252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7634","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f369c50d18194712bd4ff5024563bd6baf775e72297d99dda9aa0b2d053763f1","sha256:701f731ccf353467f295f5c41db4cdec89df7ba61189cf2c481b7f0bc1504d08"],"state_sha256":"9b4faf19aab2c186ef02e0efba48828769e4a26926d99759963dd0976d1f333f"}